If x+1/x = 7 then what is the value of x-1/x?
Answers
Answer:
If X+(1/X)=7, what is the value of X√X+(1/X√x)?
Hi,
If you know formula of (a+b)^3 then you can easily solve this problem.
Ok i am solving
Let's start
Given
x+1/x=7
And we want to find x√x+1/x√x=?
ok
First if we will do cube of (x+1/x)^3 and then we will get
(x+1/x)^3= x^3+(1/x)^3+2*x*(1/x){x+1/x}=7^3
After that we get
x^3+(1/x)^3+2(x+1/x)=343
We know that value of x+1/x=7
Put value and get
x^3+1/x^3+2*7=343
x^3+1/x^3=343–14=329
Now
(x√x+1/x^x)^2= x^3+1/x^3+2
=329+2=331 ans.
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What is the value of (x^2-1/x^2) if (x+1/x) =2√5
x+1/x=7;
=(x^2+1)/x=7:=>
=x^2–7x+1=0 —eq 3
=((x^2+2x+1)/x)-2=7
=((x+1)^2)/x=9
=x+1/x^(1/2)=3
=x+1=3x^(1/2) ——eq 1
x*x^(1/2)+(1/x*x^(1/2))=(x^3+1)/x*x^(1/2);
=(x+1)(x^2-x+1)/x*x^(1/2) —eq 2
from eq 1 we get (x+1)/x^(1/2)=3 so
putting above value in eq 2 we get
3*(x^2-x+1)/x ;
=3*(x^2–7x+1)/x+3*6x/x
now putting eq 3 in above equation we get=>
=3*(0)/x+3*6
=18 ans
Answer:
x+1/x=7
=> (x+1/x)^2=7^2=49
=> (x-1/x)^2+4.x.1/x=49
=> (x-1/x)^2+4=49
=> (x-1/x)^2=49-4
=> (x-1/x)^2=45
=> (x-1/x)=√45=√(3×3×5)
=> x-1/x=3√5